The 30-06 shoots CTBST right around 1/2" at 200 yds and that is a sporter barrel from Adams & Bennett (back when they did savage prefit) that I paid about $70 for it brand new. Back then their regular price were around $100. Never heard anything bad about their barrels... You dont have to break the bank...
The beauty of savage is that you can keep the old barrel (unless it is all shot out), get you a new barrel in the new cartridge that tickles your fancy, do the barrel change in your garage (no smith needed, we are here for you), bolthead change, mag change (if needed) and you have a new rifle. Want to go back to the .308 because whatever? take this new setting down, put the old one back and there you go... There is a table somewhere in this site where you can look at the boltheads by size and see which caliber is compatible with it and not even having to change the bolthead when switching barrels...
I went from 30-06 to 7mm rm and I thought I would never go back to 30-06. I got another action and set that one for the 30-06 because some how I was feeling "undressed" without it.... It's back to shoot clover leaves with a new bullet/load (cant get the CTSBT anywhere to try that old load). With that one action you can pretty much shot everything (single shot that is) under the sun that is standard shank. You might want to look in the future for a long action, that way you should be able to shoot your LA cartridges in that one and your SA cartridges on the action you have now and have better luck at having a repeater.
Savage are more than just a good cheap gun, they have potential to be turned in almost any bolt gun you like...
Good luck!